It's not often the audience at a gig can claim to be there against the odds, but it was true of the 700 people crowded into the Tate Modern's Turbine Hall. The announcement of Kraftwerk's residency at the gallery caused unprecedented chaos: angry fans besieged the venue after the Tate's ticket office was unable to cope with the demand. Five hours before the gig started, there were still a handful of frozen optimists waiting outside for returns.

Perhaps that accounted for the almost palpable air of disbelieving excitement before Kraftwerk appeared onstage, which made for a stark contrast with the reception Kraftwerk got when they first tried playing this music in Britain. Thirty-eight years ago, for their first British tour, hardly anyone bothered to turn up, while the music press of the day apparently sent Basil Fawlty along to review them: "Garbage floating down the polluted Rhine," offered the NME, in a review under the headline "This Is What Your Fathers Fought to Save You From".

If the xenophobia seems unforgivable, it's perhaps a little easier to understand the journalists' failure to grasp that they were in the presence of a band that would one day prove so influential, it's hard to work out what pop music would sound like without them.

The album that formed the centrepiece of this performance, 1974's Autobahn, was audibly the sound of Kraftwerk finding their feet. On the one hand, the title track introduced what you might call the classic Kraftwerk style: a droll but warm celebration of one of the modern world's everyday technological marvels, which simultaneously demonstrated a keen melodic ear, a wry attitude to rock history – its lyrics are a very Teutonic homage to the Beach Boys – and a rhythmic sensibility rather funkier than the band's detached image suggests. The latter facet was very much emphasised by the reworked version they performed here.

On the other hand, the album's B-side featured a last outing for the kind of acoustic instruments that would subsequently become verboten in Kraftwerk's world. The prospect of one of the middle-aged gentlemen onstage suddenly whipping out a descant recorder, the better to recreate Morgenspaziergang (Morning Walk), is a weirdly appealing one, but it didn't happen last night. Instead the quartet remained almost motionless behind their identical neon-lit workstations: what precisely they were doing up there, or indeed who some of them were – Ralf Hütter is now Kraftwerk's only original member – remains something of a mystery.

Instead, they relied on the 3D visuals spilling from the screen behind them to engage the audience. These were beautifully done and occasionally flatly astonishing: the lyrics of The Robots hung over the crowd's head, and there were audible gasps when a satellite careered out of the screen during Spacelab.

But in truth, Kraftwerk's music remains utterly captivating in itself. With the Autobahn album dispatched, they concentrated on rolling out the classics. In theory, music that was considered impossibly futuristic 30 years ago should have dated, yet it audibly hasn't. Some of the material had been given a nip and a tuck for the 21st century: once a beautiful wide-eyed hymn to science, Radioactivity has grown gradually darker and more troubled over the years, and now comes with references to the Fukushima nuclear disaster and lyrics in Japanese.

But Kraftwerk's timelessness has less to do with subtle updating than the quality of the songs they wrote. Neon Lights, from 1978, one of the few songs that sounded the same here as it does on record, was as wistfully beautiful as ever. What was striking about 1981's Computer Love wasn't the discreet contemporary makeover, or even how prescient the lyrics about human communication via computers turned out to be, but what a perfect pop song it is.

You could ask if it's entirely fitting that a band who once seemed so forward-looking they made their UK TV debut not on Top of the Pops but Tomorrow's World now appear consumed by their past; Hütter seems less interested in making new music than in curating their back catalogue via grand live spectacles. But the quality of the music is beyond question, the spectacles are genuinely spectacular: somehow, in a world packed with heritage acts playing their back catalogues, Kraftwerk still feel unique.